I am totally lost on how to do this... can anyone help?
What does it mean? I tried to understand what it means before proof but am totally clueless
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1Assume the antecedent and assume Pa. From it, by exists-intro, derive a contradiction.– Mauro ALLEGRANZANov 22, 2019 at 7:37
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2 Answers
¬∃xP(x)→(P(a)→Q(a))
What does it mean? I tried to understand what it means before proof but am totally clueless
It says: P(a)→Q(a) is true, if P(x) holds for no x.
So why would P(a)→Q(a) be true when that is assumed?
@GrahamKemp is correct. The statement says that if P(x) holds for no member of the universe of discourse, then P(a)->Q(a).
Recall that the truth table for the material conditional informs us that a material conditional statement is true when the antecedent is false.
So the proof is relatively easy:
